Direct extrapolation of a causal signal using low-frequency and early-time data based on matrix equations

We provide direct methods to extrapolate the early-time and the low-frequency response of a causal signal simultaneously in the time and frequency domains. We show that, in the discrete domain, the extrapolation from integral equations introduced by P.M. van den Berg et al. (see APS-URSI, 2005) is equivalent to linear matrix equations. We demonstrate the feasibility of the using the conjugate gradient method and fast Fourier transform (CGM-FFT) in the discrete version. Furthermore, we provide a more efficient method, the singular value decomposition (SVD). Finally, a numerical example of an electrically large structure is presented and a comparison between the present and the previous methods is demonstrated.